A new probabilistic finite element formulation for reliability analysis

In the application of the first-order second moment (FOSM) method to problems also involing the finite element method, the gradients of the limit state function with respect to the basic random variables need to be calculated. In principle, these calculations can be from repeated or modified application of the probabilistic finite element routine. In practical problems, however, the number of basic random variables may be very large and therefore the computation of the gradients is often very expensive. This is particular true in the FOSM analysis since the required computation of the gradient vector at each iteration step in the optimization algorithm is proportional to the number of basic random variables. To reduce CPU time without affecting the accuracy, a new formulation which can be used for the gradients calculations is developed in this paper. A direct comparison with other methods suggests that the new formulation is able to reduce significantly the CPU time and storage space requirements in the calcalation.